Re: st: RE: regression: fade rate residual income

That explanation is clearer than your earlier messages in terms of
what you intend to achieve, but whether your objective makes sense is
less clear: not enough information is provided on that issue.

The model you (appear to) propose is simply a pooled regression over
your panel of firms and years. Thus,

reg residual_income L.residual_income

should give you one single estimate for b1 (the coefficient on lagged
residual income) for your entire (unbalanced) sample. Indeed, for
what you have described, -rollreg- (or -rolling-) is exactly *not*
what you want to do. (It can be used to create a time series of
cross-sectional estimates of b1 (a different estimate for b1 per
year), for example.)

Some comments, however:

1. Any (firm, year) pair that is missing will not be included in the
regression. So Stata already automatically takes care of your
concern about missing consecutive observations in computing b1. This
is a consequence of having -xtset- (or, equivalently, -tsset-) your
data, so Stata constructs the lagged values correctly. (You can test
this claim by making a copy of your data that only includes (say)
even years, then try estimating your model again. It should fail to
produce an estimate, since L.residual_income is undefined for every
even-yeared value of residual_income in this synthetic data set.)

2. What you call a "fade rate" is probably more generally known as an
"autoregressive parameter". Some textbooks may discuss the "rate of
decay" implied by the value of the autoregressive parameter. The
larger is b1, the longer it takes for the effects of any given shock
to e(i, t+1) to dissipate from the residual_income variable. Hence,
b1 is also known as a "measure of persistence" of the shocks to e(i, t
+1).

3. It is not obvious that a pooled OLS estimator for b1 is most
appropriate. As you have a panel data structure, you might as well
try to productively exploit it. I don't know what your exposure to
panel data estimators might be, but a large number of textbooks will
cover this topic, even at the intermediate/advanced undergraduate
level. (This is particularly true in econometrics, which one might
reasonably guess is fairly close to your research area given you have
data on firms.) The basic question to ask yourself in deciding what
estimator to use is what do you hypothesize are the properties of
your error term, e(i, t+1)? Once you have some familiarity with some
basic panel data estimators, take a look at the -xt- commands for
Stata, starting with -xtreg-.

4. That said, you have a lagged endogenous regressor in your
equation. Depending on how you model the error term and what your
purposes are, that could be a significant problem. The issues
involved with lagged endogenous regressors ("dynamic panel data") are
more advanced and only some graduate-level econometrics textbooks
cover them. In Stata 10, see -xtdpd- and related commands for more
information.

Dear Nick (statalisters),
Thank you for your time. Let me be more clear this time.

I would like to examine the autoregressive properties of abnormal
earinings (=residual income) (first order abnormal earnings
autoregression). So I want to use a pooled analysis with one lag,
i.e. residual_income (i, t+1) = b0 + b1 * residual_income(i, t) + e
(i, t+1), where i is a specific company ("name" as identifier) and
t is the year of the observation ("year"). What I want to get is a
fade rate b1 , which describes the reversal of residual_income. b1
should be one single value in order to predict future residual
incomes in another sample ( i.e. residual_income next year equals
b1 times residual income this year). I expect b1 to be about 0.7
(b0=0).

When I say the regression should run over every two consecutive
years for a company I mean that the regression should ignore cases,
in which there is more than one year between two observations,
because b1 should be the fade rate of residual_income from one year
to the following year.
The identifier for company is "name" and the year is given by
"year". I used:

Well, I don't know whether my idea is an appropiate way to solve
this problem and to get one single b1. Perhaps someone can help me,
whether this is an appropiate way to solve this problem and to get
one single value of b1 and how to get rid of the gaps (because -
rollreg-from SSC does not support gaps in the data).

The most obvious is that -rollreg- from SSC [please remember to
explain
where user-written programs you discuss come from] does not
support data

with gaps. When you -tsset- your data you should have seen a comment
that your data include gaps.
The next is what you are trying to do. If I read this correctly, you

want to look at regressions for pairs of values within each panel.
That

gives you at most two distinct data points and you should be able to

solve for the coefficients directly. You will get perfect fits,
except
when points coincide when regression will be indeterminate. Also,
there

is no question of an error term.
On the other hand, I doubt that I am reading you correctly.

You posted on this topic a week ago. In response both Michael
Hanson and
I hinted that you may need to explain what you expect in more
detail to

get better answers.
Nick
n.j.cox@durham.ac.uk
GBrenner1@gmx.de
I would like to run a regression on residual_income. I have yearly

observations of residual income for firms. The year is given in
variable

"year", the identifier for firm is "name".
I'd like to run the regression residual_income(year) = b0 + b1 *
residual_income(year-1) + e The regression should run on

"residual_income" over every two consecutive years ("year") within
each

identifier "name" (whenever there are values for at least two
consecutive years for a given name).
I used the following:
drop if missing(residual_income)
tsset name year
rollreg residual_income l.residual_income, move(2) stub(a)

I hope this command will do what I want but unfortunately Stata
always